"To have an individual member of Congress dictate the agenda for the rulemaking and the schedule of an independent agency is verboten. That's a very bad thing to accommodate," Unger said in an interview with "Closing Bell."

"I think the chairman is completely right to stick to her guns on this. She is very interested in investor protection, I can assure you," she added.

In her letter, Warren argued White's refusal "serves the narrow interests of powerful executives who would prefer to hide their expenditures of company money to advance their own personal ideologies."

When last December's government funding bill prevented the SEC from "finalizing" a rule regarding the disclosure of political contributions, Warren joined dozens of other Democratic lawmakers to remind White that the bill did not prevent the SEC from at least discussing or developing a rule for political spending disclosure to be finalized at a future time. Even then, Warren said, White refused to act.

He noted there are already disclosure rules in place, and that the senator's issue is really with the Supreme Court's decision on Citizens United, which allowed for unlimited political spending by corporations.

"There's no question that Sen. Warren is staking out a position as the spiritual guru or godfather or godmother of the Democratic Party, pulling it to the left. And Elizabeth Warren doesn't like business, doesn't like corporations, she doesn't like banks," he said. "This is a shot across the bow."